# Definition:Compound Statement

## Definition

A compound statement is a statement which results from the application of one or more logical connectives to a collection of simple statements.

### Substatement

A substatement of a compound statement is one of the statements that comprise it.

### Ill-Formed Compound Statement

The substatements in a compound statement, which are joined by a connective, may be compound statements themselves.

It is clearly necessary that the interpretation of such a compound statement is unambiguous.

A compound statement is said to be ill-formed if it is ambiguous as to how its substatements are grouped by the action of the connectives.

For example, in natural language:

I would like some juice or water with ice.

can mean either:

I would like some juice, or water with ice.

or:

I would like some juice with ice, or water with ice.

## Also defined as

Some sources define a compound statement, in the context of symbolic logic, as a statement form other than:

logical not
conjunction
disjunction
conditional
biconditional.

Such is the approach of 1946: Alfred Tarski: Introduction to Logic and to the Methodology of Deductive Sciences, who separately categorises the truth tables of those five statement forms as fundamental.

Hence any statement form which is not one of those fundamental five is (implicitly) defined as being compound.

## Also known as

A compound statement can also be referred to as:

a compound sentential function
a compound sentence
a molecular sentence.

## Examples

### Napoleon

Napoleon is dead and the world is rejoicing

is a compound statement whose substatements are:

and:

The world is rejoicing.

### Shape of Eggs

If all eggs are not square then all eggs are round

is a compound statement whose substatements are:

All eggs are not square

and:

All eggs are round.

### Barometer

If the barometer falls then either it will rain or it will snow

is a compound statement whose substatements are:

The barometer falls
It will rain
It will snow.

## Also see

• Results about compound statements can be found here.